CONCEPT DIABETES: Analytical pipeline
Introduction
CONCEPT-DIABETES
CONCEPT-DIABETES is part of CONCEPT, a coordinated research project initiative under the umbrella of REDISSEC, the Spanish Research Network on Health Services Research and Chronic Conditions] [www.redissec.com], that aims at analyzing chronic care effectiveness and efficiency in a number of cohorts built on real world data (RWD). In the specific case of CONCEPT-DIABETES, the focus will be on assessing the effectiveness of a set of clinical practice actions and quality improvement strategies at different levels (patient-level, health-care provider level and health system level) on the management and health results of patients with type 2 diabetes (T2D) using process mining methodology.
It is a population-based retrospective observational study centered on all T2D patients diagnosed in four Regional Health Services within the Spanish National Health Service, that includes information from all their contacts with the health services using the electronic medical record systems including Primary Care data, Specialist Care data, Hospitalizations, Urgent Care data, Pharmacy Claims, and also other registers such as the mortality and the population register. We will assess to what extent recommended interventions from evidence-based guidelines are implemented in real life and which are their effects on health outcomes. Process mining methods will be used to analyze the data, and comparison with standard methods will be also conducted.
Cohort
The cohort is defined as patients with type 2 diabetes:
Inclusion criteria: Patients that, at 2017-01-01 or during the follow-up from 2017-01-01 to 2022-12-31, had active health card (active TIA - tarjeta sanitaria activa) and one of the inclusion codes given in the ‘inclusion code list (’T90’ if CIAP-2, ‘250’ if ‘CIE-9CM’ or ‘E11’ if CIE-10-ES) and none of the exclusion codes given in the exclusion codes list (‘T89’ if CIAP-2, ‘250.01’ if CIE-9CM, ‘250.03’ if CIE-9CM, ‘250.11’ if CIE-9CM, ‘250.13’ if CIE-9CM, ‘250.21’ if CIE-9CM, ‘250.23’ if CIE-9CM, ‘250.31’ if CIE-9CM, ‘250.33’ if CIE-9CM, ‘250.41’ if CIE-9CM, ‘250.43’ if CIE-9CM, ‘250.51’ if CIE-9CM, ‘250.53’ if CIE-9CM, ‘250.61’ if CIE-9CM, ‘250.63’ if CIE-9CM, ‘250.71’ if CIE-9CM, ‘250.73’ if CIE-9CM, ‘250.81’ if CIE-9CM, ‘250.83’ if CIE-9CM, ‘250.91’ if CIE-9CM, ‘250.93’ if CIE-9CM or ‘E10’ if CIE-10-ES) in the clinical records of primary care.
Exclusion criteria: Patients that had one the codes in exclusion code lists (‘T90’ if CIAP-2, ‘250’ if ‘CIE-9CM’ or ‘E11’ if CIE-10-ES) and none of the exclusion codes given in the exclusion codes list (‘T89’ if CIAP-2, ‘250.01’ if CIE-9CM, ‘250.03’ if CIE-9CM, ‘250.11’ if CIE-9CM, ‘250.13’ if CIE-9CM, ‘250.21’ if CIE-9CM, ‘250.23’ if CIE-9CM, ‘250.31’ if CIE-9CM, ‘250.33’ if CIE-9CM, ‘250.41’ if CIE-9CM, ‘250.43’ if CIE-9CM, ‘250.51’ if CIE-9CM, ‘250.53’ if CIE-9CM, ‘250.61’ if CIE-9CM, ‘250.63’ if CIE-9CM, ‘250.71’ if CIE-9CM, ‘250.73’ if CIE-9CM, ‘250.81’ if CIE-9CM, ‘250.83’ if CIE-9CM, ‘250.91’ if CIE-9CM, ‘250.93’ if CIE-9CM or ‘E10’ if CIE-10-ES) during their follow-up or patients with no contact with the health system from 2017-01-01 to 2022-12-31.
Study period: 2017-01-01 until 2022-12-31.
Treatment guidelines
One of the main intermediate outcome indicators to which clinical guidelines pay special attention is a good glycaemic control, since its absence is clearly related to micro and macrovascular complications. In clinical practice, suboptimal glycaemic control can be mainly attributed to two main reasons: the patients’ non-adherence to prescribed treatment; and the healthcare providers’ clinical or therapeutic guidelines’ non-adherence.
Treatment decisions are based on glycated hemoglobin measurements. In this context the redGDPS foundation provides DM2 treatment algorithm, a diagram that aims to help professionals to quickly and easily choose the most appropriate treatment for people with diabetes.
Running code
The python libraries used are:
Code
import sys
import pm4py, datetime, subprocess
import pandas as pd
import numpy as np
import itertools
import matplotlib.pyplot as plt
import textdistance
import gensim.corpora as corpora
from tqdm import trange, tqdm
from scipy.spatial.distance import squareform
from scipy.cluster.hierarchy import fcluster, linkage, dendrogram
from sklearn.cluster import AgglomerativeClustering
from sklearn.feature_extraction.text import TfidfVectorizer
from yellowbrick.cluster import KElbowVisualizer
from pm4py.objects.petri_net.obj import PetriNet, Marking
from pm4py.visualization.decisiontree import visualizer as tree_visualizer
from pm4py.algo.decision_mining import algorithm as decision_mining
from pm4py.visualization.petri_net import visualizer
from gensim.models import LdaModel
from datetime import datetime
from datetime import timedeltaThe R libraries used are:
Code
pacman::p_load(tidyverse,
lubridate,
mongolite,
jsonlite,
ggplot2,
bupaR,
processmapR,
dplyr,
DiagrammeR,
DiagrammeRsvg,
rsvg,
here)Data preprocessing and event log creation
For using process mining an event log is needed. The sort of functions below take data model’s treatment and parameter tables to create an event log of glycated hemoglobin measures and treatment of patients. Glycated hemoglobin measurement events are divided into two different states, those that have a value inferior that 7.5 and the others. Therefore, these events do not have any duration. In the case of treatments on the other hand a duration period exists. For treatments events definition it is based on drugs dispensing and a fixed time period after the dispensing date of the last dispensing date of the same drug if the dispensing is regularly produced . Functions below make an event log taking some assumptions such as that each dispensation should last 30 days.
Code
def evlog_creation(treat_df, param_df, code2drug):
'''Eventlog creation from datamodel's tables.
Args:
treat_df (dataframe): datamodel's treatment table
param_df (dataframe): datamodel's parameter table
code2drug (dataframe): ATC codes traslation to names
Returns:
df (dataframe): event log
ADNI: ANTIDIABETICOS NO INSULINICOS
The treatment of type 2 diabetes mellitus with ADNI includes a wide range of
drugs which, depending on their drugs which, according to their mechanisms of
action, can be grouped as follows:
Increased endogenous insulin sensitivity:
o Biguanides: metformin (MET).
o Thiazolidinediones: pioglitazone (PIO).
Increased endogenous insulin secretion/release:
o Sulfonylureas (SU).
o Meglitinides: repaglinide (REP)
Reduction of digestive glucose absorption:
o Alpha-glucosidase inhibitors.
o Vegetable fiber and derivatives.
Incretin effect enhancers.
o Inhibitors of DPP-4 (iDPP-4).
o GLP-1 analogues (aGLP-1).
Inhibitors of renal glucose reuptake
o SGLT-2 inhibitors (iSGLP-2)
'''
# definir los tipos de medicamentos a analizar
col_atc = 'atc_code'
col_id = 'patient_id'
col_date = 'dispensing_date'
col_event = 'Event'
treat_df = treat_df.sort_values(by = [col_id,col_date ],
ascending = [True, True])
treat_df.index = range(len(treat_df))
treat_df[col_event] = [code2drug.get(treat_df[col_atc][c],{'class' : 'ERROR'}
).get( 'class','ERROR2').replace('+','&')
if treat_df[col_atc][c].startswith(
'A') else None for c in range(len(treat_df[col_atc])) ]
treat_df = treat_df.drop(labels=[i for i in range(len(treat_df)) if
treat_df[col_event][i] in [None,'ERROR','ERROR2']],
axis=0)
treat_df.index = range(len(treat_df))
treat_df = treat_df[[col_id,col_date,col_atc,col_event]]
treat_df = treat_df.sort_values(by = [col_id,col_date ],
ascending = [True, True])
treat_df.rename(columns = {col_date:'date'}, inplace = True)
treat_df = treat_df[[col_id,'date',col_event]]
######################
col_param = 'param_name'
col_value = 'param_value'
col_date = 'param_date'
param_df = param_df.sort_values(by = [col_id,col_date ],
ascending = [True, True])
param_df.index = range(len(param_df))
param_df = param_df.drop(labels=[i for i in range(len(param_df)) if
param_df[col_param][i]!='hba1c'],axis=0)
param_df[col_value] = ['HBA<75' if i<7.5 else 'HBA>75'
for i in list(param_df[col_value])]
param_df.rename(columns = {col_value: col_event,col_date:'date'},
inplace = True)
param_df = param_df[[col_id,'date',col_event]]
df = pd.concat([param_df,treat_df])
df = df.sort_values(by = [col_id, 'date'], ascending = [True, True])
df.index = range(len(df))
df['date'] = pd.to_datetime(df['date'], format='%Y-%m-%d')
df['cycle'] = 'start'
df['actins'] = list(df.index)
patient_list = sorted(set(df[col_id]))
df['nid'] = [patient_list.index(df[col_id][n]) for n in range(len(df))]
df_ = df.copy()
df_['cycle'] = 'end'
for n in range(len(df_)):
if 'HBA' in df_[col_event][n]:
continue
df_['date'][n] += timedelta(days=30)
df = pd.concat([df,df_])
df = df.sort_values(by = [col_id, 'actins','cycle'],
ascending = [True, True, False])
return df
def evlog_transformation(df):
''' eventlog's transformation into a more useful format
Args:
df (dataframe): raw event log
Returns:
evlog (dataframe): transformed event log
'''
evlog = pd.DataFrame()
id_list = list(set(df['patient_id']))
for id in tqdm(id_list):
nid = list(df['nid'][df['patient_id']==id])[0]
date_min = min(set(df['date'][df['patient_id']==id]))
date_max = max(set(df['date'][df['patient_id']==id]))
dd = [date_min + timedelta(days=x)
for x in range((date_max-date_min).days + 1)]
ev_list = ['_']*len(dd)
for act in set(df['actins'][df['patient_id']==id]):
ini = list(df['date'][np.logical_and(df['actins']==act,
df['cycle']=='start')])[0]
fin = list(df['date'][np.logical_and(df['actins']==act,
df['cycle']=='end')])[0]
ev = list(df['Event'][np.logical_and(df['actins']==act,
df['cycle']=='start')])[0]
ev_list[dd.index(ini):dd.index(fin)+1] = [ev_list[n]+'+'+ev
for n in range(dd.index(ini),
dd.index(fin)+1)]
for n in range(len(ev_list)):
ev_list[n] = ev_list[n].replace('_+','')
if 'HBA<75' in ev_list[n]:
ev_list[n] = 'HBA<75'
elif 'HBA>75' in ev_list[n]:
ev_list[n] = 'HBA>75'
ev_list[n] = '+'.join(sorted(set(
ev_list[n].replace('&','+').split('+'))))
dic_log = {'patient_id': [id],
'date': [dd[0]],
'Event': [ev_list[0]],
'nid': [nid]}
for n in range(1,len(ev_list)):
if ev_list[n]!=ev_list[n-1]:
dic_log['patient_id'].append(id)
dic_log['date'].append(dd[n-1])
dic_log['Event'].append(ev_list[n-1])
dic_log['nid'].append(nid)
dic_log['patient_id'].append(id)
dic_log['date'].append(dd[n])
dic_log['Event'].append(ev_list[n])
dic_log['nid'].append(nid)
dic_log['patient_id'].append(id)
dic_log['date'].append(dd[-1])
dic_log['Event'].append(ev_list[-1])
dic_log['nid'].append(nid)
evlog_ = pd.DataFrame.from_dict(dic_log)
evlog_ = evlog_.drop(
evlog_[np.logical_and(evlog_.duplicated(keep=False),
np.logical_and(evlog_['Event']!='HBA<75',
evlog_['Event']!='HBA>75')
)].index)
evlog = pd.concat([evlog,evlog_])
evlog = evlog.sort_values(['patient_id','date'])
evlog.index = range(len(evlog))
evlog['cycle'] = ['start','end']*int(0.5*len(evlog))
evlog['actins'] = [n//2 for n in range(len(evlog))]
return evlog
def evlog_correction(df):
''' eventlog's correction to avoid some errors
Args:
df (dataframe): event log
Returns:
df (dataframe): corrected event log
'''
#correction to eliminate events after hemoglobin measurement that are
#the continuation of the previous treatment and not the new treatment.
#Example: If a patient has 'A' treatment and because of hemoglobin's
# measure they change their treatment to 'B', originally their
# trace could appear as A>measure>A+B>B, but the true trace
# should be A>measure>B. Therefore, in a fixed period time
# after each measurement, if we detect that mistake we delete
# it.
t_dif = timedelta(days=14)
for t in range(3):
df_ = df[df['cycle']=='start']
for id in set(df_['patient_id']):
trace = list(df_['Event'][df_['patient_id'] == id])
trace_t = list(df_['date'][df_['patient_id'] == id])
if 'HBA>75' in trace or 'HBA<75' in trace:
ind = [i for i in range(len(trace)) if trace[i] =='HBA>75'
or trace[i] == 'HBA<75']
for i in ind:
try:
if (np.in1d(trace[i-1].split('+'),
trace[i+1].split('+')).all()) and (
np.in1d(trace[i+1].split('+'),
trace[i+2].split('+')).all()) and (
# trace[i-1]!=trace[i+2]) and (
trace_t[i+2]-trace_t[i+1]<t_dif):
actin = int(df_['actins'][
np.logical_and(df_['patient_id']==id,
df_['date']==trace_t[i+1])])
df = df.drop(
list(df[df['actins']==actin].index))
trace_ = trace
for n_e in range(i,len(trace_)):
if trace_[n_e]!=list(df['Event'][df['patient_id'] == id][
df['cycle']=='start'])[n_e]:
break
trace_[n_e] = '*('+trace_[n_e]+')*'
elif (np.in1d(trace[i-1].split('+'),
trace[i+1].split('+')).all()) and (
np.in1d(trace[i+2].split('+'),
trace[i+1].split('+')).all()) and (
trace[i-1]!=trace[i+2]) and (
trace_t[i+2]-trace_t[i+1]<t_dif):
actin = int(df_['actins'][np.logical_and(df_['patient_id']==id,
df_['date']==trace_t[i+1])])
df = df.drop(list(df[df['actins']==actin].index))
trace_ = trace
for n_e in range(i,len(trace_)):
if trace_[n_e]!=list(df['Event'][df['patient_id'] == id][
df['cycle']=='start'])[n_e]:
break
trace_[n_e] = '*('+trace_[n_e]+')*'
except:
continue
#correction to delete transition treatments.
#Example: If a patient has 'A' treatment and because of a unknown
# reason they change their treatment to 'B', originally their
# trace could appear as A>A+B>B, but the true trace should be
# A>B. Therefore, if that sequence occurs in a fixed period
# of time, we delete the transition treatment.
for id in set(df['patient_id']):
status = True
while status:
trace = list(df['Event'][np.logical_and(df['patient_id'] == id,
df['cycle'] == 'start')])
trace_t = list(df['date'][df['patient_id'] == id])
if len(trace)<=2:
status = False
for i in range(len(trace)-2):
if (np.in1d(trace[i].split('+'),
trace[i+1].split('+')).all()) and (
np.in1d(trace[i+2].split('+'),
trace[i+1].split('+')).all()) and (
trace[i+2]!=trace[i]) and (
trace_t[2*i+4]-trace_t[2*i+2]<t_dif):
df['date'][np.logical_and(df['patient_id']==id,
df['date']==trace_t[2*i+4])
] = trace_t[2*i+2]
actin = int(df['actins'][np.logical_and(df['patient_id']==id,
df['date']==trace_t[2*i+3])])
df = df.drop(list(df[df['actins']==actin].index))
trace_ = trace
for n_e in range(len(trace_)):
try:
if trace_[n_e]!=list(df['Event'][df['patient_id'] == id][
df['cycle']=='start'])[n_e]:
break
except:
break
trace_[n_e] = '*('+trace_[n_e]+')*'
break
if i==len(trace)-3:
status = False
break
#event compaction.
#Example: If a patient has 'A' treatment and they are dispensing 'A'
# drug multiple times, their trace could appear as A>A>A>A,
# but the true trace should appear as 'A' treatment lasting
# its corresponding time. Therefore, if the difference between
# the last day and the first day of two consecutive same
# treatments is less than a fixed period of time, two events
# are jointed in one with the first day of the first event as
# initial date and last day of the last event as the end date.
for id in set(df['patient_id']):
status = True
while status:
trace = list(df['Event'][np.logical_and(df['patient_id'] == id,
df['cycle'] == 'start')])
trace_t = list(df['date'][df['patient_id'] == id])
if len(trace)==1:
status = False
for i in range(len(trace)-1):
if (trace[i]==trace[i+1]) and (trace_t[2*i+2]-trace_t[2*i+1]<t_dif) :
df['date'][np.logical_and(df['patient_id']==id,
df['date']==trace_t[2*i+1])
] = trace_t[2*i+3]
actin = int(df['actins'][
np.logical_and(df['patient_id']==id,df['date']== trace_t[2*i+2])])
df = df.drop(list(df[df['actins']==actin].index))
trace_ = trace
for n_e in range(i,len(trace_)):
try:
if trace_[n_e]!=list(df['Event'][df['patient_id'] == id][
df['cycle']=='start'])[n_e]:
break
except:
break
trace_[n_e] = '*('+trace_[n_e]+')*'
break
if i==len(trace)-2:
status = False
break
df.index = range(len(df))
return df
def preprocessing(treat_df_path='./inputs/dm_treat_df.csv',
param_df_path='./inputs/dm_param_df.csv',
code2drug_path='./inputs/diabetes_drugs.csv',
output_file='./outputs/eventlog_raw.csv'):
'''Preprocessing and event log obtention
Args:
treat_df_path (str): datamodel's treatment table's path
param_df_path (str): datamodel's parameter table's path
code2drug_path (str): drugs' and their codes' info's table's path
'''
treat_df = pd.read_csv(treat_df_path)
param_df = pd.read_csv(param_df_path)
code2drug = pd.read_csv(code2drug_path,index_col=0).to_dict()
evlog_0 = evlog_creation(treat_df, param_df, code2drug)
evlog_1 = evlog_transformation(evlog_0)
evlog_2 = evlog_correction(evlog_1)
evlog_2.rename(columns = {'patient_id':'ID'}, inplace = True)
evlog_2.to_csv(output_file)Distances
One of the most important aim of process mining is to show and explain the processes. However, the great variety of traces does not allow us to draw any clear conclusions and it is often necessary to simplify our data. Another option that we can do before simplifying, to avoid the excessive losing of information and give another perspective to the analysis, is to cluster the traces and to analyze them by cluster. To do that we have to measure somehow the differences between the traces, the distance between them. This is not evident if we take into account that traces are categorical sequences of different lengths. Nevertheless, there are some distances that we can use to this task: edit distances, vector term similarity, LDA based distances, dynamic time warping, embedding based distances… Some of them are shown below as functions to calculate the distance matrix of traces:
Code
####### EDIT DISTANCE #######
def calculate_dm_ED(traces,measure_f):
'''Calculate distance matrix with some edit distance.
Args:
traces (list): patients' traces
measure: some edit distance function
Returns:
dm: distance matrix
'''
id2word = corpora.Dictionary(traces)
traces_e = [[id2word.token2id[t[n]] for n in range(len(t))] for t in traces]
len_t = len(traces_e)
dm = np.zeros((len_t,len_t), dtype = float)
same = measure_f(traces_e[0],traces_e[0])
for i in trange(len_t):
dm[i][i] = same
for j in range(i+1,len_t):
d_ij = measure_f(traces_e[i],traces_e[j])
dm[i][j] = d_ij
dm[j][i] = d_ij
if same == 1:
dm = 1 - dm
return dm
####### TERM VECTOR SIMILARITY #######
def calculate_dm_TV(traces):
'''Calculate distance matrix with term vector similarity.
Args:
traces (list): list of traces
Returns:
dm (array): distance matrix
vectorizer: TfidfVectorizer
X: traces vectorized with TfidVectorizer
'''
corpus = [' '.join(t) for t in traces]
vectorizer = TfidfVectorizer(tokenizer=str.split)
X = vectorizer.fit_transform(corpus)
print('calculatin dm ...')
dm = np.asarray(np.matmul(X.todense(),X.todense().T))
dm = 1 - dm.round(decimals=4)
return dm, vectorizer, X
####### LDA BASED DISTANCE #######
def calculate_dm_LDA(traces,T=10):
'''Calculate distance matrix with LDA model.
Args:
traces (list): list of traces
T (int): number of topics of LDA model
Returns:
dm (array): distance matrix
lda_model: LdaModel
id2word (dict): tokenized events as keys and events by values
'''
# Create Dictionary
id2word = corpora.Dictionary(traces)
# Term Document Frequency
corpus = [id2word.doc2bow(text) for text in traces]
# Make LDA model
lda_model = LdaModel(corpus=corpus,
id2word=id2word,
num_topics=T,
alpha = 1,
eta = 'auto',
random_state = 123)
get_c_topic = np.array(
lda_model.get_document_topics(corpus,minimum_probability = -0.1))
sigma = np.asarray([[get_c_topic[i][j][1]
for j in range(T)] for i in range(len(corpus))])
sigma2 = np.asarray(np.matmul(sigma,sigma.T))
len_t = len(traces)
dm = np.zeros((len_t,len_t), dtype = float)
same = sigma2[0][0]/np.sqrt(sigma2[0][0]*sigma2[0][0])
for i in trange(len_t):
dm[i][i] = same
for j in range(i+1,len_t):
d_ij = sigma2[i][j]/np.sqrt(sigma2[i][i]*sigma2[j][j])
dm[i][j] = d_ij
dm[j][i] = d_ij
dm = 1-dm
return dm, lda_model, id2wordClustering
Once the distance matrix is obtained, we can proceed with the clustering. Each clustering method has its characteristics and its peculiarities, so we cannot choose whatever method we want. For example, we have to consider that our distances do not comply with the triangle inequality so they cannot be considered metrics. Another consideration is that we have a distance matrix and not a data frame in which we apply directly the method. A hierarchical clustering algorithm seems to be a good choice in our case because in addition to the above it allows to choose the optimal number of clusters.
The next code box contains two different functions to choose the optimal number of clusters:
Code
def dendogram(dm,output_png='./outputs/dendogram.png'):
'''Plot and save dendogram.
Args:
dm (array): distance matrix
output_png (str): saved dendogram's path
'''
dm_condensed = squareform(dm)
matrix = linkage(
dm_condensed,
method='average'
)
sys.setrecursionlimit(10000)
dn = dendrogram(matrix)
sys.setrecursionlimit(1000)
plt.title('Dendrogram')
plt.ylabel('Distance')
plt.xlabel('Patients traces')
plt.savefig(output_png)
plt.clf()
def kelbow(dm,elbow_metric='distortion',locate_elbow=False,
output_path='./outputs/'):
'''Plots to choose optimal clusters.
Args:
dm (array): distance matrix
elbow_metric (str): name of the method
locate_elbow (boolean): True if want to return optimal number of clusters
Returns:
k_opt (int)(optional): optimal number of clusters according to method
'''
model = AgglomerativeClustering(metric = "precomputed",
linkage = 'average')
# k is range of number of clusters.
visualizer_ = KElbowVisualizer(model,
k=(2,50),
timings=False,
xlabel = 'cluster numbers',
metric=elbow_metric,
locate_elbow=locate_elbow)
# Fit data to visualizer
output_file = output_path+elbow_metric+'.png'
visualizer_.fit(dm)
# Finalize and render figure
visualizer_.show(output_path=output_file,clear_figure=True)
k_opt=None
if locate_elbow:
k_opt = visualizer_.elbow_value_
return k_optDepending on the results of the clustering we may need to focus our analysis in the biggest clusters and forget those clusters that contains too less traces. The next function is made for that:
Code
def small_cluster_filter(log,min_traces=30,col_id='ID',col_clust='cluster'):
'''Filter smallest clusters' traces.
Args:
log (dataframe): event log
min_traces (int): minimum number of traces in the resulted clusters
col_id (str): patients id column's name in df_
col_clust (str): clusters column's name in df_
Returns:
filtered_log (dataframe): event log without clusters with les than
min_traces number of traces
'''
drop_clust = [i for i in set(log[col_clust]) if
len(set(log[col_id][log[col_clust]==i]))<min_traces]
filtered_log = log.drop(log[log[col_clust].isin(drop_clust) == True].index)
filtered_log.index = range(len(filtered_log))
return filtered_log
The function to clust is shown in the code below:
Code
def clust(clust_n,dist_matrix,df_,id2trace,patients,id_col='ID',
ev_col='Event',date_col='date',output_xes='./outputs/eventlog.xes',
output_csv='./outputs/eventlog.csv'):
'''clusterize distance matrix.
Args:
clust_n (int): number of clusters obtained
dist_matrix (array): distance matrix
df_ (dataframe): event log
id2trace (dict): patient ids as keys and their traces as values
patients (list): patients' ids in same order as in dm
id_col (str): patients id column's name in df_
ev_col (str): events column's name in df_
date_col (str): events dates column's name in df_
'''
model = AgglomerativeClustering(n_clusters=clust_n,
metric = "precomputed",
linkage = 'average')
model.fit(dist_matrix)
labels = model.labels_
cluster_list ={id: labels[traces.index(id2trace[id])
] for id in patients}
df_['cluster'] = [cluster_list[df_[id_col][i]] for i in range(len(df_))]
df_.to_csv(output_csv)
df_filtered = small_cluster_filter(df_)
df_filtered.to_csv(output_csv.replace('.csv','_filtered.csv'))
df_xes = pm4py.format_dataframe(df_,
case_id=id_col,
activity_key=ev_col,
timestamp_key=date_col)
event_log = pm4py.convert_to_event_log(df_xes)
pm4py.write_xes(event_log, output_xes)
df_filtered_xes = pm4py.format_dataframe(df_filtered,
case_id=id_col,
activity_key=ev_col,
timestamp_key=date_col)
event_log_filtered = pm4py.convert_to_event_log(df_filtered_xes)
pm4py.write_xes(event_log_filtered,output_xes.replace('.xes','_filtered.xes'))Descriptive analysis
The implementation below is made to show the most frequent traces in each cluster:
Code
def make_data_dict(log,top_k,col_id):
'''Obtain most frequent traces and their statistics
Args:
log (dataframe): event log
top_k (int): number of traces want to show
col_id (str): patients id column's name in df_
Returns:
data_dict (dict): traces as keys and ther statistics as values
'''
len_id = len(set(log[col_id]))
log_freq = pm4py.stats.get_variants(log)
freq_list = [(t,log_freq[t],len(t)) for t in set(log_freq.keys())]
trace = [list(t[0]) for t in sorted(freq_list, key=lambda x:
(len_id-x[1],x[2]))[:top_k]]
cases = [t[1] for t in sorted(freq_list, key=lambda x:
(len_id-x[1],x[2]))[:top_k]]
top_k = min(top_k,len(cases))
percentage = [100*cases[c]/len_id for c in range(top_k)]
cum_percentage = [sum(percentage[:p+1]) for p in range(top_k)]
data_dict = {"Trace": trace,
"Percentage": percentage,
"Cases": cases,
"Cumulative Percentage": cum_percentage}
return data_dict
def update_color_dict(color_dict,data_dict):
'''update of the color dict to include new events
Args:
color_dict (dict): events as keys and colors as values
data_dict (dict): traces as keys and ther statistics as values
Returns:
color_dict (dict): events as keys and colors as values
'''
cmap = plt.cm.get_cmap('tab20')
for event in set(itertools.chain.from_iterable(data_dict['Trace'])):
if event not in color_dict and len(color_dict)==20:
cmap = plt.cm.get_cmap('tab20b')
if event not in color_dict:
try:
color_dict.update({event:cmap(len(color_dict))})
except:
color_dict.update({event:cmap(2*(len(color_dict)-20))})
return color_dict
def trace_plotter(data_dict,color_dict,acronym, output_file, font_size=10,
percentage_box_width=0.8,size=(15,9)):
'''configuration of the trace_explorer plot
Args:
color_dict (dict): events as keys and colors as values
data_dict (dict): traces as keys and their statistics as values
acronym (dict): events as keys and their acronyms as values
output_file (str): figure's path
font_size (int): font size
percentage_box_width (float): event boxes' width
size (tuple): figure's size
'''
fig, ax = plt.subplots(figsize=size)
percentage_position = max(len(t) for t in data_dict["Trace"]
) + percentage_box_width*3 +0.5
for row, (trace, percentage,cases,cum_percentage
) in enumerate(zip(data_dict["Trace"],
data_dict["Percentage"],
data_dict["Cases"],
data_dict["Cumulative Percentage"]),
start=1):
for col, acr in enumerate(trace, start=1):
ax.add_patch(plt.Rectangle((col - 0.5, row - 0.45), 1, 0.9,
facecolor=color_dict[acr],
edgecolor='white'))
ax.text(col,
row,
acr,
ha='center',
va='center',
color='white',
fontsize = font_size,
fontweight='bold')
ax.add_patch(plt.Rectangle((
percentage_position -percentage_box_width*2.5,
row - 0.45), percentage_box_width, 0.9,
facecolor='grey', edgecolor='white'))
ax.text(percentage_position-percentage_box_width*2,
row,
f'{percentage:.2f}%',
ha='center',
va='center',
color='white',
fontsize = font_size+2)
ax.add_patch(plt.Rectangle((
percentage_position - percentage_box_width*1.5,
row - 0.45), percentage_box_width, 0.9,
facecolor='grey', edgecolor='white'))
ax.text(percentage_position-percentage_box_width,
row,
f'{cases}',
ha='center',
va='center',
color='white',
fontsize = font_size+4)
ax.add_patch(plt.Rectangle((percentage_position - percentage_box_width*0.5,
row - 0.45), percentage_box_width, 0.9,
facecolor='grey', edgecolor='white'))
ax.text(percentage_position,
row,
f'{cum_percentage:.2f}%',
ha='center',
va='center',
color='white',
fontsize = font_size+2)
ax.set_xlim(0.5, percentage_position+0.5)
ax.set_xticks(range(1, int(percentage_position-1)))
ax.set_ylabel('Traces',fontsize = font_size+3)
ax.set_ylim(len(data_dict["Trace"]) + 0.45, 0.55) # y-axis is reversed
ax.set_yticks([])
ax.set_xlabel('Activities',fontsize = font_size+3)
handles = [plt.Rectangle((0, 0), 0, 0, facecolor=color_dict[acr],
edgecolor='black', label=acronym[acr])
for acr in acronym if acr in set(
itertools.chain.from_iterable(data_dict['Trace']))]
ax.legend(handles=handles,
bbox_to_anchor=[1.02, 1.02],
loc='upper left',
fontsize = font_size+6)
for dir in ['left', 'right', 'top']:
ax.spines[dir].set_visible(False)
plt.tight_layout()
plt.savefig(output_file)
plt.close()
def trace_explorer(evlog_file='./outputs/eventlog.xes',top_k=5, id_col='ID',
ev_col='Event',date_col='date',clust_col='cluster',
color_dict={}):
'''Plot each clusters most frequent traces
Args:
evlog_file (str): events as keys and colors as values
top_k (int): traces as keys and their statistics as values
id_col (str): patients id column's name in evlog_file
ev_col (str): events column's name in evlog_file
date_col (str): events dates column's name in evlog_file
clust_col (str): cluster column's name in evlog_file
color_dict (dict): events as keys and colors as values
'''
log_ = pm4py.read_xes(evlog_file)
log_ = log_.sort_values([id_col,date_col])
log_ = log_[log_['cycle']=='start']
for clust in set(log_[clust_col]):
log = log_[log_[clust_col]==clust]
len_id = len(set(log[id_col]))
acronym = {t:t for t in sorted(set(log[ev_col]))}
data_dict = make_data_dict(log,top_k,id_col)
color_dict = update_color_dict(color_dict, data_dict)
trace_plotter(data_dict,color_dict,acronym,
'./outputs/trace_%i.png' % clust)
return color_dictTo get the process maps of each cluster next R functions can be used:
Code
load_csv_log <- function(evlog_csv,case_id="ID",activity_id="Event",
lifecycle_id="cycle", activity_instance_id="actins",
timestamp="date"){
eventlog = read.csv(evlog_csv, header=TRUE, sep = ",")
eventlog = eventlog[order(eventlog$ID),]
#Para transformar fecha a un formato con el que podemos trabajar
eventlog$date = as.POSIXct(eventlog$date, tz = "", format="%Y-%m-%d" ,
tryFormats = c("%Y/%m/%d",
"%Y/%m/%d"),
optional = FALSE)
evLog = eventlog %>%
mutate(resource = NA) %>%
mutate(cycle = fct_recode(cycle, "start" = "start","complete" = "end")) %>%
eventlog(
case_id = case_id,
activity_id = activity_id,
lifecycle_id = lifecycle_id,
activity_instance_id = activity_instance_id,
timestamp = timestamp,
resource_id = 'resource'
)
return(evLog)
}
make_process_map <- function(log,t_freq,output_file){
log %>%
filter_activity_frequency(percentage = 1) %>% # show only most frequent
filter_trace_frequency(percentage = t_freq) %>%
process_map(type_nodes = performance(mean,units='days'),
type_edges = frequency('relative_case'),
sec_edges = performance(mean,units='days'),
render = T) %>%
export_svg %>%
charToRaw %>%
rsvg_png (output_file,width=2000)
}
process_map_by_cluster <- function(evLog,t_freq){
for (clust in unique(evLog$cluster)) {
log <- evLog %>%
filter(cluster == clust)
make_process_map(log,t_freq,here("outputs",sprintf(
"evlog_pm_cluster_%d.png", clust)))
}
}Conformance checking
Conformance checking is ‘A’ technique used to check process compliance by comparing event logs for a discovered process with the existing reference model (target model) of the same process. Basing on the DM2 treatment algorithm previous shown, with a software called Carassius , we created the next Petri Net that is going to be useful as treatment guidelines in reference to glycated hemoglobin measures to patients with frailty.
Fitness is the metric that measures how much a trace is distanced from a given process model, or from the guidelines in this case. There are different methods to calculate this metric but in the code below is used the aligned fitness. Since in this metric the initial marking and the final marking have to be fixed we included the events ‘INI’ and ‘FIN’ in the Petri Net and in each trace. Adding this artificial events allows us to compare all traces fitness in the same conditions.
Code
def id2fitness(log ,net, initial_marking, final_marking, clust_col='cluster',
date_col='date',ev_col='Event'):
'''Obtain traces fitness
Args:
log (dataframe): event log
net: petri net
initial_marking: initial place in the petri net
final_marking: final place in the petri net
clust_col (str): cluster column's name in log
date_col (str): events dates column's name in log
ev_col (str): events column's name in log
Returns:
df (dataframe): traces, their clusters and their fitnesses
'''
at_l = []
rt_l = []
name_l = []
clust_l = []
for name in set(log['case:concept:name']):
log2 = log.drop(log.index[log['case:concept:name'] !=name])
ini = log2.iloc[0,:].copy()
ini[date_col] = ini['time:timestamp'] = ini[date_col
]-timedelta(days=1)
ini[ev_col] = ini['concept:name'] = 'INI'
ini['@@index'] = ini['@@index']-1
ini['actins'] = ini['actins']-1
fin = log2.iloc[-1,:].copy()
fin[date_col] = fin['time:timestamp'] = fin[date_col
]+timedelta(days=1)
fin[ev_col] = fin['concept:name'] = 'FIN'
fin['@@index'] = fin['@@index']+1
fin['actins'] = fin['actins']+1
log2 = log2.append(ini)
log2 = log2.append(fin )
log2 = log2.sort_values(date_col)
log2.index = range(len(log2))
#alignment
aligned_traces = pm4py.conformance_diagnostics_alignments(
log2, net, initial_marking, final_marking)
name_l.append(name)
at_l.append(aligned_traces[0]['fitness'])
clust_l.append(int(list(log2[clust_col])[0]))
df = pd.DataFrame()
df['ID'] = name_l
df['aligned_fitness'] = at_l
df[clust_col] = clust_l
return dfIn the next function is shown a boxplot function to show clusters’ fitness distribution.
Code
def conformance(xes_file,pn_file,ini_place='place11',fin_place='place10',
date_col='date',ev_col='Event',clust_col='cluster',
output_png='./outputs/fitness_by_cluster.png',
output_csv='./outputs/fitness_by_cluster.csv'):
'''Barplot of the fitness of each cluster
Args:
xes_file (dataframe): event log's path
pn_file: petri net's path
ini_marking: initial place in the petri net
fin_marking: final place in the petri net
date_col (str): events dates column's name in log
clust_col (str): cluster column's name in log
ev_col (str): events column's name in log
output_png (str): created figure's path
output_csv (str): created csv's path
'''
log = pd.DataFrame(pm4py.read_xes(xes_file))
log = log[log['cycle']=='start']
log = log.sort_values(date_col)
log.index = range(len(log))
net, initial_marking, final_marking = pm4py.read_pnml(pn_file)
initial_marking = Marking()
initial_marking[list(net.places)[[str(p) for p in net.places].index(ini_place)]] = 1
final_marking = Marking()
final_marking[list(net.places)[[str(p) for p in net.places].index(fin_place)]] = 1
df = id2fitness(log,net,initial_marking,final_marking,clust_col,date_col,ev_col)
df.to_csv(output_csv)
data = [list(df['aligned_fitness'][df[clust_col]==i])
for i in sorted(set(df[clust_col]))]
fig = plt.figure(figsize =(10, 7))
# Creating axes instance
ax = fig.add_axes([0, 0, 1, 1])
# Creating plot
bp = ax.boxplot(data,labels=[i for i in sorted(set(df[clust_col]))])
plt.xlabel("Clusters")
plt.ylabel("Aligned Fitness")
# show plot
plt.savefig(output_png,bbox_inches='tight')
Decision mining
Decision mining allows to analyze the event transitions in different part of processes. With another words, we can measure patients’ characteristics or their relevance in a specific place of the passed petri net. The next function makes a decision tree explaining how patients characteristics are taking into account. Moreover it shows a boxplot of the relevance of each feature in the decision tree obtained with mean decrease impurity which calculates each feature importance as the sum over the number of splits (across all tress) that include the feature, proportionally to the number of samples it splits.
Code
def decision_tree_pn_place(patients_df,
col_id = 'patient_id',
features_list = ['age','sex'],
event_log_file="./outputs/eventlog.xes",
pn_file="./inputs/FRAG_HBA.pnml",
place2analyze='place9',
ini_place='place11',
fin_place='place10'):
'''Decision tree and features importances in selected place of PN
Args:
patients_df (dataframe): patients data wanted to analyze
col_id (str): patients id column's name in df
features_list (list): features wanted to analyze
event_log_file (str): event log's path
pn_file (str): petri net's path
place2analyze (str): place wanted to analyze in petri net
ini_place (str): initial place in the petri net
fin_place (str): final place in the petri net
'''
log = pm4py.read_xes(event_log_file)
log = log[log['cycle']=='start']
log = log[['concept:name','time:timestamp','case:concept:name']]
log = log.sort_values(by = ['case:concept:name','time:timestamp' ],
ascending = [True, True])
log.index = range(len(log))
for name in set(log['case:concept:name']):
log2 = log.drop(log.index[log['case:concept:name'] !=name])
ini = log2.iloc[0,:].copy()
ini['time:timestamp'] = ini['time:timestamp']-timedelta(days=1)
ini['concept:name'] = 'INI'
fin = log2.iloc[-1,:].copy()
fin['time:timestamp'] = fin['time:timestamp']+timedelta(days=1)
fin['concept:name'] = 'FIN'
log = log.append(ini)
log = log.append(fin )
log = log.sort_values(['case:concept:name','time:timestamp'])
log.index = range(len(log))
features_list += [col_id]
patients_df = patients_df[features_list]
log_patients = log.merge(patients_df,left_on='case:concept:name',
right_on=col_id,how='left')
net, initial_marking, final_marking = pm4py.read_pnml(pn_file)
initial_marking = Marking()
initial_marking[list(net.places)[[str(p)
for p in net.places].index(ini_place)]] = 1
final_marking = Marking()
final_marking[list(net.places)[[str(p)
for p in net.places].index(fin_place)]] = 1
X, y, class_names = decision_mining.apply(log_patients,
net,
initial_marking,
final_marking,
decision_point=place2analyze)
clf, feature_names, classes = decision_mining.get_decision_tree(log_patients,
net,
initial_marking,
final_marking,
decision_point=place2analyze)
gviz = tree_visualizer.apply(clf, feature_names, classes)
gviz.save(filename='decision_tree',
directory='outputs')
visualizer.view(gviz)
importances = clf.feature_importances_
tree_importances = pd.Series(importances, index=feature_names)
fig, ax = plt.subplots()
tree_importances.plot.bar(ax=ax)
ax.set_title("Feature importances using MDI")
ax.set_ylabel("Mean decrease in impurity")
fig.tight_layout()
fig.savefig('./outputs/barplot_features_importance.png')Multivariate logistic regression model
The link between guideline adherence, in terms of performed process measures, and clinical outcomes is a highly demanded issue in diabetes care. Logistic regression models can be used to predict different outcomes such as probability of hospitalization, treatment complication probability or probability of death, while as the same time a treatment adherence is analyzed. For that a variable that measures treatment adherence is needed for example fitness of patients’ traces.
Results
Event log’s creation and description
These results have been carried out with a set of synthetic data previously generated according to data model. After some preprocessing we obtain an event log that can be reproduced in the below process map Figure 2. There is shown how the events are connected, the mean number of days patients spent in each event (or treatment), percentage of patients who made each transition and the mean number of days it took to make the transition. However, a spaghetti map is obtained and nothing can be concluded. Therefore, we have to simplify the process map and for example only show the most frequent traces covering 20% of the event log as in Figure 3. Moreover, in Figure 4 we show percentage of patients’ traces each activity is present.
Clustering traces
Once the set of traces to analyze are selected, there is a need to choose a distance measure to clustering. In this example Jaccard similarity is chosen to calculate the distance matrix.
When distance matrix is acquired, we are able to cluster. However, the number of clusters have to be fixed before. With these figures we are able to conclude what could be the optimal number of clusters.
Choosing 18 as the optimal number of clusters, too small clusters appear. Excluding those clusters of less than 30 traces, to avoid having clusters of low representation, process maps and the most frequent traces of the eight clusters that remain are the followings.
Conformace checking
Once traces are clusterized, with a boxplot is easy to show that each cluster’s behavior with respect to the treatment guides is different. Comparing traces with Figure 1, calculating the fitness (1 being perfect match with the petri net and 0 being the lowest possible fitness) of each trace and grouping by cluster results in Figure 14.
Decision mining
In Figure 15 is shown how patients’ age and sex (being 0 females’ value and 1 males’ one) would influence in prescribing three drugs based treatment. More features could have been added but for simplicity we included those two.
Variables relevance in the previous decision tree is indicated in Figure 16. As we can see, categorical variables are divided into as many parts as the number of categories there are and variables’ total relevance is the sum of its categories’ values.
Multivariate logistic regression model with fitness
Using fitness as treatment adherence measuring and some static characteristics we made a multivariate logistic regression model to predict some interesting outcome. In the next example, for simplicity, we choose fiteness, age, sex and copayment to try to predict mortality, and the summary of it is:
Call:
glm(formula = death ~ age + sex + copayment + aligned_fitness,
family = binomial, data = df)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.285 -1.180 1.083 1.169 1.289
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.029043 0.219930 -0.132 0.895
age 0.001926 0.001881 1.024 0.306
sexmale -0.075646 0.103837 -0.729 0.466
copayment 0.139521 0.103867 1.343 0.179
aligned_fitness -0.209462 0.455527 -0.460 0.646
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 2066.9 on 1490 degrees of freedom
Residual deviance: 2063.3 on 1486 degrees of freedom
(977 observations deleted due to missingness)
AIC: 2073.3
Number of Fisher Scoring iterations: 3